$$\mathop {Lim}\limits_{x \to \infty } {{{x^3} - \cos x} \over {{x^2} + {{\left( {\sin x} \right)}^2}}} = \_\_\_\_\_\_.$$

A bag contains 10 white balls and 15 black balls. Two balls drawn in succession. The probability that one of them is black the other is white is

Let A be the set of all nonsingular matrices over real numbers and let * be the matrix multiplication operator. Then

The number of elements in the power set $$P(S)$$ of the set $$S = \left\{ {\left\{ \phi \right\},1,\left\{ {2,3} \right\}} \right\}$$ is